Typical tools used by laboratory investigators involve the use of least squares methods, quadratic programming, simplex methods, or derivative free methods (Nelder-Mead) to fit models to experimentally obtained data. Functional models are usually resolved by such methods. Other data, such as complex combinations of known or reference spectra are more readily resolved by matrix methods such as Singular Value Decomposition. In such cases, the "singular values" signal the relative importance of the component spectra in the decomposition of the complex measured spectra. Such methods can be developed from mathematical software packages, such as MATLAB, for a number of computing platforms. As a result, such mehtods are portable to any machine for which MATLAB has been developed. The purpose of this project is to provide NIH investigators with mathematical tools for insight, analysis, and solution of complex equations that arise in the modeling of biological systems. To facilitate these efforts, LAS developed mathematical methods that are accessible to investigators from many disciplines. Software packages that result from these developments are made available to the research community as general research tools. Advice on the use of certain commercial mathematical software packages is also offered. This project is currently involved with applications in several diverse areas, e.g., deconvolution of bilirubin-pheuobarbital and heme biosynthesis and clearance; circular dichrosim spectra modeling in thermal unfolding of sevine pepsinogen; resolution of forward rate binding measurements in hemoglobin; regression analysis of oxygenation isotherms; rapid scanning spectrophotometry for oxygen binding to hemoglobin; bacteriorhodopsin recovery from laser flash; and cytochrome-a-a3 kinetics.